Thread: Area of shaded region. Limits in question.

I'm having an issue with a particular question in that the limits are not being used (only the upper limit is being used). If I use only the upper limit, I get the correct answer, but if I use both limits, the area comes in -ve and becomes wrong.

I would just like to know why.

The equation of the following curve is: x^3-3x^2-9x+27.
The integrated equation becomes: x^4/4 - x^3 -9x^2/2 +27x.

Here's the figure:



Using x=3 gives us 33.75 as the area. This is the answer.
But what about x=0? If I use this and subtract the results, I get -47.25.

Any explanation would be helpful.

What do you get if the function x^4/4 - x^3/3 - 9x^2/2 + 27x is evaluated at x = 0? What happens when you subtract this answer from 33.75?

Thanks for the reply.

I just found and realized the mistake I was making after looking at your post. I was constantly taking, even for the x=0 limit, the x=3 limit at the 27x portion. So, instead of taking x=0 at 27x which would become 27(0) or 0, I was taking x=3 which would become 27(3) or 81, and subtracting that from the x=3 evaluation. It's going to be simply 33.75 - 0.

Well, like I've said earlier, I'm not good at mathematics and I tend to make these simple mistakes frequently without even realizing it.